Idea:
Magic items are items imbued with magic. They have levels roughly equal to the different levels at which spells can be cast. They can be pretty strong and they're reliable.
Legendary items are not magical; not in the same way at least. Legendary items dwarf most magical items by measure of power, but they draw power from belief and faith. Their power is the power that people believe they have. It can change over time, growing or shrinking in power, and many powerful people perpetuate rumors to strengthen or weaken legendary items.
Artifacts are similar to legendary items, but they are tied only to the belief of the people that made them. A culture's belief in an artifact gives it power, and othef peoples disbelief does not impact it.
Mythical items are also similar to legendary items. Only, mythical items do not exist. Perhaps they did once, or perhaps they began only as a rumor or a hope. They manifest only to those their legends most directly affect and only in times of need.